Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy.

Area of Science:

• Mechanical Engineering
• Signal Processing
• Data Analysis

Background:

• Standard Dynamic Mode Decomposition (DMD) faces challenges with rank order selection and mode component identification.
• Existing methods struggle with denoising and feature extraction in complex mechanical signals.

Purpose of the Study:

• To develop a novel algorithm for denoising and feature extraction in multi-component coupled noisy mechanical signals.
• To address the limitations of traditional Dynamic Mode Decomposition (DMD) in determining optimal dimensionality reduction and identifying relevant modes.

Main Methods:

• Utilized a sparse optimization method with a non-convex penalty function to determine the optimal dimensionality reduction space in DMD.
• Employed multiscale permutation entropy to assess the complexity of each DMD mode.
• Implemented thresholding to discard noise-corresponding modes and reconstruct the signal.

Main Results:

• The proposed algorithm successfully identified optimal DMD modes and effectively separated noise components.
• Applied to rolling bearing signals, the method demonstrated superior performance compared to wavelet transform.
• Validated on both simulated and experimental data, confirming its effectiveness in noise reduction and fault feature extraction.

Conclusions:

• The novel DMD-based algorithm offers a robust solution for denoising and fault feature extraction in mechanical signals.
• The method shows significant promise for applications in condition monitoring and diagnostics of rotating machinery.
• This approach overcomes key limitations of standard DMD, enhancing its practical applicability.